Aitken-Steffensen-type methods for nonsmooth functions (I)


We study the convergence of the Aitken-Steffensen method for solving a scalar equation \(f(x)=0\). Under reasonable conditions (without assuming the differentiability of \(f\)) we construct some auxilliary functions used in these iterations, which generate bilateral sequences approximating the solution of the considered equation.


Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)


nonlinear equations in R; Aitken-Steffensen method.


PDF-LaTeX file on the journal website.

Cite this paper as:

I. Păvăloiu, Aitken-Steffensen-type methods for nonsmooth functions (I), Rev. Anal. Numér. Théor. Approx., 31 (2002) no. 1, pp. 109-114.

About this paper

Print ISSN


Online ISSN



Balázs, M., A bilateral approximating method for finding the real roots of real equations, Rev. Anal. Numér. Théor. Approx., 21, no. 2, pp. 111-117, 1992,

Casulli, V. and Trigiante, D., The convergence order for iterative multipoint procedures, Calcolo, 13, no. 1, pp. 25-44, 1977,

Cobzaş, S., Mathematical Analysis, Presa Universitară Clujeană, Cluj-Napoca, 1997 (in Romanian).

Ostrowski, A. M., Solution of Equations and Systems of Equations, Academic Press, New York, 1960.

Păvăloiu, I., On the monotonicity of the sequences of approximations obtained by Steffensens’s method, Mathematica (Cluj), 35 (58), no. 1, pp. 71-76, 1993.

Păvăloiu, I., Bilateral approximations for the solutions of scalar equations, Rev. Anal. Numér. Théor. Approx., 23, no. 1, pp. 95-100, 1994,

Păvăloiu, I., Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences, Calcolo, 32, no. 1-2, pp. 69-82, 1995,

Traub, F. J., Iterative Methods for the Solution of Equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964.


Related Posts